Events at The University of Manchester
  • University home
  • Events
  • Home
  • Exhibitions
  • Conferences
  • Lectures and seminars
  • Performances
  • Events for prospective students
  • Sustainability events
  • Family events
  • All Events

Logic Seminar - Paul Shafer (Leeds)

Dates:25 May 2022
Times:15:00 - 16:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Adults, Alumni, Current University students
See travel and contact information
Add to your calendar

More information

  • Department of Mathematics

Other events

  • In category "Seminar"
  • In group "(Maths) Maths seminar series"
  • In group "(Maths) Logic"
  • By Department of Mathematics

Title: Cohesive powers of linear orders

Abstract: A cohesive power of a computable structure is an effective analog of an ultrapower, where a cohesive set acts as an ultrafilter.  We compare the properties of cohesive powers to those of classical ultrapowers.  In particular, we investigate what structures arise as the cohesive power of B over C, where B varies over the computable copies of some fixed computably presentable structure A and C varies over the cohesive sets.

Let omega, zeta, and eta denote the respective order-types of (N, <), (Z, <), and (Q, <).  We take omega as our computably presentable structure, and we consider the cohesive powers of its computable copies.  If L is a computable copy of omega that is computably isomorphic to the standard presentation (N, <), then all of L's cohesive powers have order-type omega + (zeta x eta), which is familiar as the order-type of countable non-standard models of PA.

We show that it is possible to realize a variety of order-types other than omega + (zeta x eta) as cohesive powers of computable copies of omega.  For example, we show that there is a computable copy L of omega whose power by any Delta_2 cohesive set has order-type omega + eta.  More generally, we show that it is possible to achieve order-types of the form omega + certain shuffle sums as cohesive powers of computable linear orders of type omega.

Travel and Contact Information

Find event

Frank Adams 1 (and zoom, link in email)
Alan Turing Building
Manchester

 

Contact us

  • +44 (0) 161 306 6000

Find us

The University of Manchester
Oxford Rd
Manchester
M13 9PL
UK

Connect with the University

  • Facebook page for The University of Manchester
  • X (formerly Twitter) page for The University of Manchester
  • YouTube page for The University of Manchester
  • Instagram page for The University of Manchester
  • TikTok page for The University of Manchester
  • LinkedIn page for The University of Manchester

  • Privacy /
  • Copyright notice /
  • Accessibility /
  • Freedom of information /
  • Charitable status /
  • Royal Charter Number: RC000797
  • Close menu
  • Home
    • Featured events
    • Today's events
    • The Whitworth events
    • Manchester Museum events
    • Jodrell Bank Discovery Centre events
    • Martin Harris Centre events
    • The John Rylands Library events
    • Exhibitions
    • Conferences
    • Lectures and seminars
    • Performances
    • Events for prospective students
    • Sustainability events
    • Family events
    • All events